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More rarely, statins may cause muscle breakdown, a process called rhabdomyolysis, states Mayo Clinic. This process releases a muscle protein called myoglobin into the bloodstream, which may cause kidney damage. Other rare but serious side effects of statin use include liver damage, cognitive problems and increased blood sugar. Increased blood sugar can cause Type 2 diabetes, which can lead to nerve damage called diabetic neuropathy, according to WebMD, but statins do not directly cause diabetic neuropathy.